# Learn a Stat: Strength of Schedule (SoS)

Welcome back to Hack a Stat! In this Learn a Stat, you will find everything you need to understand SoS, an acronym that stands for Strength of Schedule.

ITALIAN VERSION

### Introduction

The Strength of Schedule, commonly called SoS, is a team statistic widely used in the USA and, more generally, where there are championships in which the teams’ schedules are different regarding the number of matches or for the opponents faced. SoS in Europe, on the other hand, loses much of its peculiarities and value, given that competitions have the same schedules for all teams. Despite this, the Strength of Schedule can also be useful in Europe: for example, you can evaluate the hardness of the teams’ run during the season or understand, in the situation of multi-phase and multiple-group competitions, the difficulty of the path taken by each team.

### Definition and starting data

As already said, SoS is an acronym that stands for Strength of Schedule.

The data required for the calculation are very simple. The only statistic required is the W% (Winning Percentage). There are variants of the SoS in which the Net Rating is used instead of the W%. The formulas and the calculation sequence remain the same, as does the meaning of the final result. The comparison scale will be instead different.

The reason why W% or Net Rating is used is very simple. SoS is used to understand how tough a team’s schedule has been. The hardness of a match is directly related to the opponent’s strength. W% and Net Rating are two stats that show how strong a team is (and therefore tough to face). The Net Rating, unlike the Winning Percentage, also takes into account how much the team’s final score gap usually is; therefore, compared to W%, it is more suitable to take this aspect into account. On the other hand, however, the SoS remains an estimate of the difficulty faced and not an accurate calculation, therefore even only the W% (very easy to find) is suitable with the calculation of this advanced statistic. In short, therefore you need:

• Opponent Winning Percentage [OppW%];
• Team Game Played [TmGP];

You can use also the Net Rating:

• Opponent Net Rating [OppNet Rtg];
• Team Game Played [TmGP];

### Formula and calculation

The calculation and the relative formulas for the SoS are relatively simple and short; however, the theories behind this process are not so simple. Let’s start with the formula:

$\mathbf{SoS=\frac{2OW%+OOW%}{3}}$

As you can see in the formula (and as you could already guess from the data listed in the previous paragraph), the team winning percentage does not appear in the formula. You do not need to know how good the team for which we are calculating the SoS is, but you are only interested in knowing the opponent skills level.

For obtaining the Overall Opponent Winning Percentage [OW%], you have to add up all the winning percentages of the opponents encountered and divide them by the number of games played by the team for which you are calculating the SoS.

$\mathbf{OW%=\frac{\sum_{i=1}^{n}OppW%_{i}}{TmGP}}$

The operation is an average of the opponents’ winning percentages. If a team has played two or more times against an opponent, its Winning Percentage must be added the same number of times. For example, if you are calculating the SoS after the first round of return of a classic European competition, you have to add up all the Winning Percentages of all the teams and add again the OppW% of the team faced on the first round of return. It is important to underline this step because OppW% is calculated on the number of games played and not on the number of opponents faced.
Another very important aspect is that the OppW% does not take into account the matches played against the team for which the SoS is being calculated. This step is crucial: in fact, the strength of an opponent cannot be calculated considering the matches played against the team under analysis.

The OOW%, on the other hand, is a more challenging thread to understand: this stat is the Overall Opponent Winning Percentage of the opponents faced by the team under analysis. With this data, you consider the toughness of the path of the opponents: doing this is very relevant because only the opponent W% could provide you the wrong information. For example, a mid-level team may have a high W% only because it has faced weak teams. Without taking this aspect into account, an inaccurate estimate of SoS can be calculated because the opponent’s force would be overestimated. To find the OOW%, you have to take the previously calculated OW%, add up them together, and then divide them by the number of games played by the team under analysis.

$\mathbf{OOW%=\frac{\sum_{i=1}^{n}OW%_{i}}{TmGP}}$

Once OW% and OOW% have been calculated, you just need to use the initial formula (also reported here) to find the SoS of the teams.

$\mathbf{SoS=\frac{2OW%+OOW%}{3}}$

This formula is actually a weighted average: the Overall Opponent Winning Percentage has a double weight than the OOW%.

As mentioned, the Net Rating can be used instead of Winning Percentages: the procedure and theories explained above remain valid also in this case.
Furthermore, there are calculation variants in which different weights are given to home and away wins: the basic OppW% and GP data will be changed based on the games played at home and away. Usually, you give greater weight to away victories, considered more challenging. The weight is at the discretion of the person who calculates. For example, if a team has lost a home game and won an away game and you want to give a weight of 1.5 to the away wins, the W% will be:

$\boldsymbol{\mathbf{}W%=\frac{0+1,5*1}{1+1,5}=0,6=60%}$

The team obtained a W% of 60% instead of the normal 50% without different weights.

Let’s see some examples to understand everything.

### How to read and analyze

Let’s consider a 6-games 4-team mini-tournament. Efes, Real Madrid, Barcelona, and Zalgiris have played it. These are the results of the six games:

First step is to calculate the OW%:

In the table above (has to be read from left to right), you can see the individual steps for calculating the OW%. The first columns show the individual calculations to find the various OppW% for each team. Take for example the Efes: the OppW% of Real is equal to 100% because, without considering the match against the Efes, it won two games out of two. Barcelona has played twice with the Efes, so you only have to consider the lost game against the Real; so OppW% is equal to 0. Lastly, the Zalgiris: following the same steps, its OppW% is also equal to 0.
The various OppW% are added up and are divided by the number of games played by the Turkish team. As you can see, Efes played twice against Barca, so the Catalan team’s OppW% is added up twice.
This procedure is performed for all participants.

Next step is to find OOW%:

The previously calculated OW% are taken and add them up based on the games played and then divide the result as done for the OW%. Efes played twice against Barca, once against Real and once against Zalgiris: the Barca’s OW% will be added twice while the ones of Zalgiris and Real Madrid only one time.
We have all the data, we can calculate the SoS:

That’s it, the Strength of Schedule is calculated. The higher the value, the greater the toughness of the schedule played. In this case, Real and Zalgiris had the most difficult runs.

The most important feature to note about the Strength of Schedule is that it is not a predictive statistic. The SoS is a statistic that refers to the matches already played by a team and does not provide any indication regarding the next matches. One aspect to keep in mind when using it.

Last consideration, when calculating the Strength of Schedule for the classic European competitions, the SoS of all the teams at the end of the season will be equal to 0.5. This is because all the teams will have faced, in the end, the same schedule.

This Learn a Stat ends here. See you soon, your friendly neighborhood Cappe!